More recently, pQG has benefited from the progress made on modern helicity amplitude methods
[1]}, [2]}, [3]}.
Within the common approach to QFT, as it is presented in most text-book, the kinematics involves the energy-momenta 4-vectors,
while the wave function for spin-1/2 and vector particles involves the Dirac spinors and polarization vectors.
However, within the Helicity formalism, one works with a unified framework, where both kinematical variables and the wave functions for
external particles are dealt using spinor variables, i.e. Weyl spinors. A variety of results that one could call "perturbative jewels" have been discovered over the years, which include, for example, the derivation of simple expressions for the maximal-helicity violating amplitudes for gluons in Yang-Mills theories (Parke-Taylor), and also for gravitons from pQG [4]}. One of the most precious result is
that some amplitudes involving gravitons can be expressed as the square of the corresponding amplitude for gluons, a result that is expressed as: \(GR=YM\times YM\) , which summarizes the relationship between gravity and Yang-Mills amplitudes. This result was derived first at tree-level using results in string theory [5]}, and is known as the KLT relations. More recently, it was found that some relations hold at loop-level, which is known as the double-copy formula or Bern-Carrasco-Johansson (BCJ) relation [6]}, [7]}.
Most progress has been made for massless theories, but more recently the massive case has also been tackled
[8]}, [9]}.
